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We develop an algorithm for single-image superresolution of remotely senseddata, based on the discrete shearlet transform. The shearlet transform extractsdirectional features of signals, and is known to provide near-optimally sparserepresentations for a broad class of images. This often leads to superiorperformance in edge detection and image representation when compared toisotropic frames. We justify the use of shearlets mathematically, beforepresenting a denoising single-image superresolution algorithm that combines theshearlet transform with sparse mixing estimators (SME). Our algorithm iscompared with a variety of single-image superresolution methods, includingwavelet SME superresolution. Our numerical results demonstrate competitiveperformance in terms of PSNR and SSIM.

Superresolution of Noisy Remotely Sensed Images Through Directional Representations